Metal-poor stars are important tools for tracing the early history of the Milky Way, and for learning about the first generations of stars. Simulations suggest that the oldest metal-poor stars are to be found in the inner Galaxy. Typical bulge surveys, however, lack low metallicity ([Fe/H] < -1.0) stars because the inner Galaxy is predominantly metal-rich. The aim of the Pristine Inner Galaxy Survey (PIGS) is to study the metal-poor and very metal-poor (VMP, [Fe/H] < -2.0) stars in this region. In PIGS, metal-poor targets for spectroscopic follow-up are selected from metallicity-sensitive CaHK photometry from the CFHT. This work presents the ~250 deg^2 photometric survey as well as intermediate-resolution spectroscopic follow-up observations for ~8000 stars using AAOmega on the AAT. The spectra are analysed using two independent tools: ULySS with an empirical spectral library, and FERRE with a library of synthetic spectra. The comparison between the two methods enables a robust determination of the stellar parameters and their uncertainties. We present a sample of 1300 VMP stars -- the largest sample of VMP stars in the inner Galaxy to date. Additionally, our spectroscopic dataset includes ~1700 horizontal branch stars, which are useful metal-poor standard candles. We furthermore show that PIGS photometry selects VMP stars with unprecedented efficiency: 86%/80% (lower/higher extinction) of the best candidates satisfy [Fe/H] < -2.0, as do 80%/63% of a larger, less strictly selected sample. We discuss future applications of this unique dataset that will further our understanding of the chemical and dynamical evolution of the innermost regions of our Galaxy.